Question: Rewrite as a simplified fraction. ${1.9\overline{63} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1963.6363...\\ 10x &= 19.6363...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1944}$ ${x = \dfrac{1944}{990}} $ ${x = \dfrac{108}{55}} \text{or} {1 \dfrac{53}{55}}$